Type in your questions on the readings for Week 2 here. Add your initials in the parentheses at the end of each of your questions.
• It is striking to me the way in which Scribner (1984) justified the use of experimental design in her socicocultural or ethonographic study of dairy workers: "contrived situations (experiments) ... help answer questions about complex phenomena which either cannot or can only with great inefficiency be answered on the basis of naturalistic observations" (p. 22). Sitatued in a sociocultural theoretical approach, is this bricolage (see Cobb (2007)) necessary? That is, is complementing an ethnographic approach with an experimental approach appropriate in all cases? Is Scribner's criteria helpful in justifying this design decision? (1/17/10 NF)
• I had some trouble seeing the activities described in both Scriber (1984) and Lave, Murtaugh, and de la Roche (1984) as "problem-solving." In both papers the problems seem too narrow. For example, in Scribner, I have trouble seeing the act of filling an order as a "problem" for a preloader. It's a routine task. The problem, in this situation, seems more likely to be along the lines of "learning to perform the task of preloading efficiently." An experienced preloader has solved the problem. A novice has not. Indeed it may be productive to view the "poor solutions" of novices as initial "solution shapes" to be refined through a process of "gap-closing" (Lave, Murtaugh, and de la Roche, 1984, p. 83). Do we have a good defintion for what is meant by a "problem" or what is meant by "problem-solving?" In designing a study, how does one choose the appropriate unit of analysis for "problems?" (1/18/10 RK)
• In Lave, Murtaugh, and de la Roche (1984), participants were asked to "think out loud" (p. 69) while they did their grocery shopping. It seems likely to me that thinking out loud would influence the cognitive processes of the participants. In addition, this thinking takes place in the presence of two observers, both of whom are well-educated. Again it seems likely that both the cognitive processes the occur and the cognitive processes that are expressed will be influenced (for example participants may feel the need to impress the observers). I wonder if there is an issue of credibility as a result? (1/18/10 RK)
• In Saxe (1988), do we know what kind of mathematics the children are learning in school? For example, are they learning only the standard algorithm for addition or are they learning grouping strategies as well? Somewhat similarly, in Lave, Murtaugh, and de la Roche (1984) was it clear what kind of questions were asked on the pencil and paper test? If exact answers were required on the test, while grocery shopping called only for solutions based on approximations and comparisons, is it inappropriate to make the comparison on p. 82? (1/18/10, RK)
• Saxe (1988) suggested that mathematics instruction should provide students with more ownership in their learning by making it functional and transparent. How is mathematics instruction in classrooms faring in terms of these suggestions? (1/18/10, JH)
• In both Saxe (1988) and Scribner (1984), what factors led the subjects to have more accurate solutions in their arithmetic problems? (1/18/10, JH)
- Janice, are you are referring to the fact that individual in-cultural-practices were tested as being superior to paper-and-pencil exams taken out of context? If so, wasn't it the actual situation of the learning in the practice that contributed to a learner's improved performance? (1/25/10 NF)
• In Scribner (1984), students were unable to perform preloaders' tasks, although the kind of mathematics students learn in that nearby high school was not made known. However, meaningful learning should be transferable to new situation. Why is it difficult for students to transfer school learning to out-of-school problem solving situations? (NA)
- I'm just curious about this notion of meaningful learning and the potential support for the notion of 'transferability' of learning across situations. One of the points that seemed to be made in this set of articles was that it is difficult to develop in-context situations in school settings. In other words, in some senses it is not possible to duplicate 'real world' problems to school situations because of the societal and cultural factors that are inherent in those in-cultural-practices. So, I've almost presented a reverse argument to your claim. That is, it's difficult to transfer in-school knowledge to real world problems studied in-school because of the social and cultural context of the institution of school. Other ideas? (1/25/10 NF)
• How can classroom learning adequately incorporate out-of-school activities to ensure a smooth transition from school to work? (NA)
- Maybe I was really addressing this question by responding to your previous question, Napthalin. What do you think? (1/25/10 NF)
• On page 27 of the Scribner article, she mentions that "different processes of comparison and solution characterize expert and novice assemblies." It is clear that with more experience comes more ability to use "visual inspection" to solve problems. One could argue that the same type of transition occurs for the candy-selling and grocery shopping situations as well. How many "work hours" are required for this transition from novice to expert? What contribution does the educational level seem to make? How do the educational level and work hours balance each other out in this transition and what are the implications for success in solving mathematical problems -- both practical and academic? (CZ)
• How do we connect the culture from an individual study, such as the candy-selling children, to American culture, including classroom culture? (JE)
- Good question, but if I may, I might answer your question with yet another question... do we really want to make this connection? What benefit would there be even if you were able to make the connection? Is some of the point of sociocultural theory the fact that the context in which it is studied is critical to the study, the kinds of questions you can ask and the answers you can get from that? (1/25/10 NF)
• Scribner identifies non-verbal processing methods that "bypass" slower, more verbal arithmetic strategies learned in school (pg. 26). Lave, Murtaugh, and de la Roche point out how economic problems often have more flexible solutions and environments that influence the problem solving process. Saxe also pointed out "regrouping strategies" based on currency values in contrast to standard algorithms learned from school (pg 19). How widespread are these types of phenomenon? (I.E.: Phenomenon where the conditions of a problem encountered during economic activity -"real life"- make it advantageous to use strategies not taught in math class.) If these phenomenon are very widespread (as I believe them to be), does this have a strong impact on public perceptions of mathematics and math education. Do either of these facts have implications for the teaching of mathematics and teaching of mathematics teachers? (JDS)
• It is striking to me the way in which Scribner (1984) justified the use of experimental design in her socicocultural or ethonographic study of dairy workers: "contrived situations (experiments) ... help answer questions about complex phenomena which either cannot or can only with great inefficiency be answered on the basis of naturalistic observations" (p. 22). Sitatued in a sociocultural theoretical approach, is this bricolage (see Cobb (2007)) necessary? That is, is complementing an ethnographic approach with an experimental approach appropriate in all cases? Is Scribner's criteria helpful in justifying this design decision? (1/17/10 NF)
• I had some trouble seeing the activities described in both Scriber (1984) and Lave, Murtaugh, and de la Roche (1984) as "problem-solving." In both papers the problems seem too narrow. For example, in Scribner, I have trouble seeing the act of filling an order as a "problem" for a preloader. It's a routine task. The problem, in this situation, seems more likely to be along the lines of "learning to perform the task of preloading efficiently." An experienced preloader has solved the problem. A novice has not. Indeed it may be productive to view the "poor solutions" of novices as initial "solution shapes" to be refined through a process of "gap-closing" (Lave, Murtaugh, and de la Roche, 1984, p. 83). Do we have a good defintion for what is meant by a "problem" or what is meant by "problem-solving?" In designing a study, how does one choose the appropriate unit of analysis for "problems?" (1/18/10 RK)
• In Lave, Murtaugh, and de la Roche (1984), participants were asked to "think out loud" (p. 69) while they did their grocery shopping. It seems likely to me that thinking out loud would influence the cognitive processes of the participants. In addition, this thinking takes place in the presence of two observers, both of whom are well-educated. Again it seems likely that both the cognitive processes the occur and the cognitive processes that are expressed will be influenced (for example participants may feel the need to impress the observers). I wonder if there is an issue of credibility as a result? (1/18/10 RK)
• In Saxe (1988), do we know what kind of mathematics the children are learning in school? For example, are they learning only the standard algorithm for addition or are they learning grouping strategies as well? Somewhat similarly, in Lave, Murtaugh, and de la Roche (1984) was it clear what kind of questions were asked on the pencil and paper test? If exact answers were required on the test, while grocery shopping called only for solutions based on approximations and comparisons, is it inappropriate to make the comparison on p. 82? (1/18/10, RK)
• Saxe (1988) suggested that mathematics instruction should provide students with more ownership in their learning by making it functional and transparent. How is mathematics instruction in classrooms faring in terms of these suggestions? (1/18/10, JH)
• In both Saxe (1988) and Scribner (1984), what factors led the subjects to have more accurate solutions in their arithmetic problems? (1/18/10, JH)
- Janice, are you are referring to the fact that individual in-cultural-practices were tested as being superior to paper-and-pencil exams taken out of context? If so, wasn't it the actual situation of the learning in the practice that contributed to a learner's improved performance? (1/25/10 NF)
• In Scribner (1984), students were unable to perform preloaders' tasks, although the kind of mathematics students learn in that nearby high school was not made known. However, meaningful learning should be transferable to new situation. Why is it difficult for students to transfer school learning to out-of-school problem solving situations? (NA)
- I'm just curious about this notion of meaningful learning and the potential support for the notion of 'transferability' of learning across situations. One of the points that seemed to be made in this set of articles was that it is difficult to develop in-context situations in school settings. In other words, in some senses it is not possible to duplicate 'real world' problems to school situations because of the societal and cultural factors that are inherent in those in-cultural-practices. So, I've almost presented a reverse argument to your claim. That is, it's difficult to transfer in-school knowledge to real world problems studied in-school because of the social and cultural context of the institution of school. Other ideas? (1/25/10 NF)
• How can classroom learning adequately incorporate out-of-school activities to ensure a smooth transition from school to work? (NA)
- Maybe I was really addressing this question by responding to your previous question, Napthalin. What do you think? (1/25/10 NF)
• On page 27 of the Scribner article, she mentions that "different processes of comparison and solution characterize expert and novice assemblies." It is clear that with more experience comes more ability to use "visual inspection" to solve problems. One could argue that the same type of transition occurs for the candy-selling and grocery shopping situations as well. How many "work hours" are required for this transition from novice to expert? What contribution does the educational level seem to make? How do the educational level and work hours balance each other out in this transition and what are the implications for success in solving mathematical problems -- both practical and academic? (CZ)
• How do we connect the culture from an individual study, such as the candy-selling children, to American culture, including classroom culture? (JE)
- Good question, but if I may, I might answer your question with yet another question... do we really want to make this connection? What benefit would there be even if you were able to make the connection? Is some of the point of sociocultural theory the fact that the context in which it is studied is critical to the study, the kinds of questions you can ask and the answers you can get from that? (1/25/10 NF)
• Scribner identifies non-verbal processing methods that "bypass" slower, more verbal arithmetic strategies learned in school (pg. 26). Lave, Murtaugh, and de la Roche point out how economic problems often have more flexible solutions and environments that influence the problem solving process. Saxe also pointed out "regrouping strategies" based on currency values in contrast to standard algorithms learned from school (pg 19). How widespread are these types of phenomenon? (I.E.: Phenomenon where the conditions of a problem encountered during economic activity -"real life"- make it advantageous to use strategies not taught in math class.) If these phenomenon are very widespread (as I believe them to be), does this have a strong impact on public perceptions of mathematics and math education. Do either of these facts have implications for the teaching of mathematics and teaching of mathematics teachers? (JDS)